Spherically symmetric Einstein-Maxwell theory and loop quantum gravity corrections

Abstract

Effects of inverse triad corrections and (point) holonomy corrections, occuring in loop quantum gravity, are considered on the properties of Reissner-Nordstr\"om black holes. The version of inverse triad corrections with unmodified constraint algebra reveals the possibility of occurrence of three horizons (over a finite range of mass) and also shows a mass threshold beyond which the inner horizon disappears. For the version with modified constraint algebra, coordinate transformations are no longer a good symmetry. The covariance property of spacetime is regained by using a \emph{quantum} notion of mapping from phase space to spacetime. The resulting quantum effects in both versions of these corrections can be associated with renormalization of either mass, charge or wave function. In neither of the versions, Newton's constant is renormalized. (Point) Holonomy corrections are shown to preclude the undeformed version of constraint algebra as also a static solution, though time-independent solutions exist. A possible reason for difficulty in constructing a covariant metric for these corrections is highlighted. Furthermore, the deformed algebra with holonomy corrections is shown to imply signature change.